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On the Hilbert kernel density estimate

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  • Devroye, Luc
  • Krzyzak, Adam

Abstract

Let X be an -valued random variable with unknown density f. Let X1,...,Xn be i.i.d. random variables drawn from f. We study the pointwise convergence of a new class of density estimates, of which the most striking member is the Hilbert kernel estimatewhere Vd is the volume of the unit ball in . This is particularly interesting as this density estimate is basically of the format of the kernel estimate (except for the log n factor in front) and the kernel estimate does not have a smoothing parameter.

Suggested Citation

  • Devroye, Luc & Krzyzak, Adam, 1999. "On the Hilbert kernel density estimate," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 299-308, September.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:3:p:299-308
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    References listed on IDEAS

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    1. Devroye, Luc & Györfi, Laszlo & Krzyzak, Adam, 1998. "The Hilbert Kernel Regression Estimate," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 209-227, May.
    2. Mack, Y. P. & Rosenblatt, M., 1979. "Multivariate k-nearest neighbor density estimates," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 1-15, March.
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    Cited by:

    1. Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.

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